During one time period, the price of rhodium increased at a rate that was proportional to the price of rhodium at that time. The price for an ounce of rhodium was 475 initially, and it quadrupled every 25 months. What was the price for an ounce of rhodium after 18 months?

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Given Information: We are given that the price of rhodium quadruples every 25 months. This means that the price is multiplied by 4 every 25 months. To find the price after 18 months, we need to determine the growth factor for 18 months.Calculate Growth Rate: Since the price quadruples every 25 months, we can express the growth rate per month as the 25th root of 4. This is because if we take this growth rate and raise it to the power of 25, we should get 4. Growth rate per month = (4)^(1/25)Apply Growth Rate: Now we need to apply this monthly growth rate to the initial price of rhodium for 18 months. This means we will raise the growth rate to the power of 18 and multiply it by the initial price. Price after 18 months = 475 * (4)^(18/25)Calculate Growth Factor: Let's calculate the growth factor for 18 months: Growth factor for 18 months = (4)^(18/25) We can use a calculator to find this value.Find Growth Factor Value: After calculating the growth factor for 18 months, we find: Growth factor for 18 months ≈ 2.6561 (rounded to four decimal places)Calculate Price After 18 Months: Now we multiply the initial price by the growth factor to find the price after 18 months: Price after 18 months = 475 * 2.6561Final Price Calculation: Calculating the price after 18 months gives us: Price after 18 months ≈ 1261.65 (rounded to two decimal places)

During one time period, the price of rhodium increased at a rate that was proportional to the price of rhodium at that time. The price for an ounce of rhodium was $475$ initially, and it quadrupled every $25$ months. What was the price for an ounce of rhodium after $18$ months?

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During one time period, the price of rhodium increased at a rate that was proportional to the price of rhodium at that time. The price for an ounce of rhodium was 475475475 initially, and it quadrupled every 252525 months. What was the price for an ounce of rhodium after 181818 months?

During one time period, the price of rhodium increased at a rate that was proportional to the price of rhodium at that time. The price for an ounce of rhodium was $475$ initially, and it quadrupled every $25$ months. What was the price for an ounce of rhodium after $18$ months?